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Questions and Answers
What does F(x) + c represent?
What does F(x) + c represent?
- Horizontal translation left
- Vertical translation down
- Vertical translation up (correct)
- Reflection over x-axis
What does F(x) - c represent?
What does F(x) - c represent?
- Horizontal translation right
- Reflection over y-axis
- Vertical translation down (correct)
- Vertical translation up
What does F(x + c) represent?
What does F(x + c) represent?
- Horizontal translation left (correct)
- Vertical compression
- Horizontal translation right
- Vertical stretch
What does F(x - c) represent?
What does F(x - c) represent?
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What does -f(x) represent?
What does -f(x) represent?
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What does F(-x) represent?
What does F(-x) represent?
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What does Af(x) represent?
What does Af(x) represent?
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What does Af(x) where A is a fraction represent?
What does Af(x) where A is a fraction represent?
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What does F(ax) represent?
What does F(ax) represent?
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What does F(ax) where A is a fraction represent?
What does F(ax) where A is a fraction represent?
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Study Notes
Vertical Translations
- F(x) + c: Indicates a vertical translation upward by c units.
- F(x) - c: Represents a vertical translation downward by c units.
Horizontal Translations
- F(x + c): Signifies a horizontal translation to the left by c units.
- F(x - c): Denotes a horizontal translation to the right by c units.
Reflections
- -f(x): Demonstrates a reflection of the graph over the x-axis, reversing the y-values.
- F(-x): Represents a reflection over the y-axis, reversing the x-values.
Vertical Transformations
- Af(x) with A > 1: Indicates a vertical stretch, making the graph taller.
- Af(x) with 0 < A < 1: Signifies vertical compression, resulting in a squished graph when A is a fraction.
Horizontal Transformations
- F(ax) with A > 1: Indicates horizontal compression, squeezing the graph closer together.
- F(ax) with 0 < A < 1: Represents a horizontal stretch, causing the graph to spread out.
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